A certain businessman wears only three different colors of shirt -- white, blue, and gray. The probability that he will wear a blue or gray shirt is 2/3. During a four-day work week, what is the probability that the businessman will wear a white shirt at least once?
There's a typo with the OA - you've got the digits in the denominator reversed.
So, let's ignore the "OA" and solve.
For complex probability questions, it's almost always quicker to solve with the "one minus" approach:
Probability (what you want) = 1 - Probability (what you don't want)
Here we want white on at least one day. So, we don't want no white shirts at all.
Since the probability of blue or grey is 2/3,
the probability of no white on any of the 4 days = (2/3)(2/3)(2/3)(2/3) = 16/81
1 - 16/81 = 65/81... done!
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